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Circumcenter of a 2D Triangle — result sheet
Find the Cartesian circumcenter and circumradius of a non-collinear triangle from its three ordered vertices.
Inputs used
Results
Visual chart
Breakdown
Calculation steps
Returned data table
Formula and methodology
Formula: For u=B-A, v=C-A, D=u_x v_y-u_y v_x, O=A+((|u|^2 v_y-|v|^2 u_y)/(2D), (u_x|v|^2-v_x|u|^2)/(2D)).
The circumcenter is the point equidistant from the three vertices. The calculator translates the triangle to vertex A, solves the perpendicular-bisector equations, and returns the center and common radius.
This result follows the calculator's declared inputs, precision, validation boundaries, and model limits.
Input contract
- Vertex A x1 — The x coordinate of vertex A.; minimum -1000000; maximum 1000000
- Vertex A y1 — The y coordinate of vertex A.; minimum -1000000; maximum 1000000
- Vertex B x2 — The x coordinate of vertex B.; minimum -1000000; maximum 1000000
- Vertex B y2 — The y coordinate of vertex B.; minimum -1000000; maximum 1000000
- Vertex C x3 — The x coordinate of vertex C.; minimum -1000000; maximum 1000000
- Vertex C y3 — The y coordinate of vertex C.; minimum -1000000; maximum 1000000
Worked example
| Input | Value |
|---|---|
| Vertex A x1 | 0 |
| Vertex A y1 | 0 |
| Vertex B x2 | 4 |
| Vertex B y2 | 0 |
| Vertex C x3 | 0 |
| Vertex C y3 | 3 |
The circumcenter is (2, 1.5) and the circumradius is 2.5.
Assumptions and limits
- The three vertices are finite points in one two-dimensional Cartesian coordinate system and are not collinear or nearly collinear.
- The result is the Euclidean circumcenter and circumradius of the triangle; no spherical geometry, unit conversion, or finite-drawing interpretation is added.
Calculator note
Source and methodology
Use the official WorldCalculate methodology policy for the source, formula, precision, and boundary standards behind this calculator.
Planning estimate, not financial, medical, legal, or professional advice. © WorldCalculate — reuse with attribution. Built and curated by Hassan ALRowaie.
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